{
 "metadata": {
  "name": ""
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# set some ipython notebook properties\n",
      "%matplotlib inline\n",
      "\n",
      "# set degree of verbosity (adapt to INFO for more verbose output)\n",
      "import logging\n",
      "logging.basicConfig(level=logging.WARNING)\n",
      "\n",
      "# set figure sizes\n",
      "import pylab\n",
      "pylab.rcParams['figure.figsize'] = (10.0, 8.0)\n",
      "\n",
      "# set display width for pandas data frames\n",
      "import pandas as pd\n",
      "pd.set_option('display.width', 1000)\n",
      "\n",
      "\n",
      "import numpy as np\n",
      "from fastlmm.pyplink.snpreader.Bed import Bed\n",
      "from fastlmm.association.PrecomputeLocoPcs import load_intersect\n",
      "from fastlmm.inference.lmm_cov import LMM as fastLMM\n",
      "\n",
      "\n",
      "bed_fn = \"../../tests/datasets/mouse/alldata\"\n",
      "pheno_fn = \"../../tests/datasets/mouse/pheno_10_causals.txt\"\n",
      "snp_reader = Bed(bed_fn)\n",
      "G, y, _, _ = load_intersect(snp_reader, pheno_fn)\n",
      "\n",
      "num = 20\n",
      "\n",
      "h2_log_delta = [1.0 / (np.exp(x) + 1) for x in np.linspace(-5, 10, num)]\n",
      "h2_linspace = np.linspace(0,0.999,num=num)\n",
      "\n",
      "lmm = fastLMM(Y=y, G=G, K=None)\n",
      "\n",
      "nll_log_delta = []\n",
      "for h2 in h2_log_delta:\n",
      "    res = lmm.nLLeval(h2=h2)\n",
      "    nll_log_delta.append(res[\"nLL\"])\n",
      "    \n",
      "nll_linspace = []\n",
      "for h2 in h2_linspace:\n",
      "    res = lmm.nLLeval(h2=h2)\n",
      "    nll_linspace.append(res[\"nLL\"])\n",
      "\n",
      "\n",
      "# scale kernel for comparison\n",
      "K = G.dot(G.T)\n",
      "K /= np.sum(np.diag(K))\n",
      "K *= K.shape[0]\n",
      "\n",
      "lmm = fastLMM(Y=y, K=K)\n",
      "\n",
      "nll_h2_norm = []\n",
      "for h2 in h2_linspace:\n",
      "    res = lmm.nLLeval(h2=h2)\n",
      "    nll_h2_norm.append(res[\"nLL\"])\n",
      "\n",
      "\n",
      "print \"min nll log-delta\", min(nll_log_delta)\n",
      "print \"min nll h2\", min(nll_linspace)\n",
      "print \"min nll h2 (norm)\", min(nll_h2_norm)\n",
      "\n",
      "    \n",
      "import pylab\n",
      "pylab.semilogx(h2_log_delta, nll_log_delta, \"-x\", label=\"log_delta\")\n",
      "pylab.semilogx(h2_linspace, nll_linspace, \"-o\", label=\"h2\")\n",
      "pylab.semilogx(h2_linspace, nll_h2_norm, \"-x\", label=\"h2_norm\")\n",
      "pylab.title(\"log space x\")\n",
      "pylab.legend(loc=\"best\")\n",
      "pylab.show()\n",
      "\n",
      "\n",
      "pylab.plot(h2_log_delta, nll_log_delta, \"-x\", label=\"log_delta\")\n",
      "pylab.plot(h2_linspace, nll_linspace, \"-o\", label=\"h2\")\n",
      "pylab.plot(h2_linspace, nll_h2_norm, \"-x\", label=\"h2_norm\")\n",
      "pylab.title(\"lin space x\")\n",
      "\n",
      "pylab.legend(loc=\"best\")\n",
      "pylab.show()\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "min nll log-delta [ 2230.4143443]\n",
        "min nll h2 [ 2751.821687]\n",
        "min nll h2 (norm) [ 2229.39506729]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "C:\\Users\\chwidmer\\Documents\\Projects\\fastlmm\\fastlmm\\association\\PrecomputeLocoPcs.py:58: DeprecationWarning: This intersect_ids is deprecated. Pysnptools includes newer versions of intersect_ids\n",
        "  warnings.warn(\"This intersect_ids is deprecated. Pysnptools includes newer versions of intersect_ids\", DeprecationWarning)\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
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61xjNb/99g+r+5a2OJK7GCSNhNsOFhkJsNluBIzOXOi6lQ59/EfEWZ87m8K8p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\n7MlT9er2fsIEW3pJTbUXnwsX4KmnYOBA+zg52ZKzceNuJFw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       "text": [
        "<matplotlib.figure.Figure at 0x9582fd0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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pvdJM3PNLGDMGwsK8PVIREfEGdxtpt/c+fshqtXLPPfeQmpqKxWLh/vvvZ9as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\nYWEwdSrs3AmtW5vzIh98EAoL7a5MRETOx8mT8NBDMH8+rF5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       "text": [
        "<matplotlib.figure.Figure at 0x1148b710>"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Conclusion: There does not seem to be an advantage in optimizing in log-space if kernels have been scaled."
     ]
    }
   ],
   "metadata": {}
  }
 ]
}